# First order circuit with DC sources

• Engineering
• Blehs
In summary, the current splits into three paths according to resistance, and does not bypass a resistor when it reaches a crossroads.
Blehs
The circuit is in the attachment, plus the values that I've managed to find out so far.

Im having problem with figuring out the voltage at t=infinity.

So far i know that when t->infinity that inductors become short circuit. It says to apply current division and then Ohm's Law as a hint, and that's where I am stuffing up.

What i would like to know is - when the switch is closed, does current NOT flow through any of the resistors afterwards? Cause when i try to trace current flow, it ends up flowing through all the resistors anyway.

I tried doing current division; 9//5 = 3.214 ohms
then 3.214 + 8 = 11.214
then 12 x [ 11.214/(6+11.214) ] to determine current through the 6 ohm resistor

multiplying that by 6 gives me 46.904 A

#### Attachments

• Circuit problem.jpg
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Current will flow through the resistors. And yes, a long time after t=0 the inductor becomes an effective short circuit.

Note that the 9 and 5 ohm resistors are not in parallel. However, when the switch is closed, note that the 9 and 8 Ohm resistors are connected at each end -- so they become parallel connected! That also places the 6 Ohm resistor in parallel with the 12A supply current. So imagine "folding" the circuit along the 5 Ohm--Inductor line. If you redraw the circuit accordingly, it should considerably simplify its appearance. See the attached figure.

The resistor network is then amenable to simplification down to a single resistance.

#### Attachments

• Fig2.gif
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Ok so BEFORE the circuit is redrawn, and there's just a single wire with no resistor on it connecting a and a' - if you were to trace the current from the 12A source wouldn't the current simply bypass the 9 ohm resistor and go through the short circuit all the way to a'? Then the current would split in two to go through the 8 and 6 ohm resistors.

In the redrawn circuit, it shows that the current actually splits 3-ways into the 8, 9 and 6 ohm resistors.

Blehs said:
Ok so BEFORE the circuit is redrawn, and there's just a single wire with no resistor on it connecting a and a' - if you were to trace the current from the 12A source wouldn't the current simply bypass the 9 ohm resistor and go through the short circuit all the way to a'? Then the current would split in two to go through the 8 and 6 ohm resistors.

Why would it bypass a perfectly good path to where it wants to go (back to the bottom terminal of the current source)? The current will split into as many paths as are made available to it, dividing according to the relative conductances,

In the redrawn circuit, it shows that the current actually splits 3-ways into the 8, 9 and 6 ohm resistors.

Yup. As it does in the pre-redrawn circuit!

I learned that when current reaches a crossroads, then the current likes to choose the path with less resistance. Since the wire is practically at zero resistance then wouldn't all current flow through the short circuit instead?

Blehs said:
I learned that when current reaches a crossroads, then the current likes to choose the path with less resistance. Since the wire is practically at zero resistance then wouldn't all current flow through the short circuit instead?

That is not quite correct.

The current divides according to the relative conductances of the paths (conductance being the inverse of resistance). By "path" we mean the entire path back to the source or to where all the paths to choose from join up again, not just to the next node in line for an individual path!

Some current flows through all paths unless one of the paths happens to be zero resistance (infinite conductance!) and bypasses all of the other paths to the current's final destination.

In the attached figure, i2 and i3 will be nonzero; Not all of the current flows through the lowest value of resistance!

#### Attachments

• Fig1.gif
1.9 KB · Views: 494
gneill said:
That is not quite correct.

The current divides according to the relative conductances of the paths (conductance being the inverse of resistance). By "path" we mean the entire path back to the source or to where all the paths to choose from join up again, not just to the next node in line for an individual path!

Some current flows through all paths unless one of the paths happens to be zero resistance (infinite conductance!) and bypasses all of the other paths to the current's final destination.

In the attached figure, i2 and i3 will be nonzero; Not all of the current flows through the lowest value of resistance!

WOW that clears up so much. Alright i get it now =] Thnx heaps for the help, will be useful for my upcoming exam in 2 days time =P

## 1. What is a first order circuit with DC sources?

A first order circuit with DC sources is a type of electrical circuit that contains only one energy storage element, such as a capacitor or inductor, and is powered by a direct current (DC) source. It is commonly used to analyze and design circuits that involve resistors, capacitors, and inductors.

## 2. What are the key components of a first order circuit with DC sources?

The key components of a first order circuit with DC sources include a DC voltage or current source, a resistor, and an energy storage element such as a capacitor or inductor. These components are connected in series or parallel and form a closed loop through which the current flows.

## 3. How do you analyze a first order circuit with DC sources?

To analyze a first order circuit with DC sources, you can use techniques such as Kirchhoff's laws, which state that the sum of the currents at any node in the circuit is equal to zero, and the sum of the voltages around any closed loop in the circuit is equal to zero. You can also use differential equations to model the behavior of the circuit over time.

## 4. What is the time constant of a first order circuit with DC sources?

The time constant of a first order circuit with DC sources is a measure of how quickly the energy storage element (capacitor or inductor) in the circuit charges or discharges. It is equal to the product of the resistance and capacitance or inductance in the circuit. A larger time constant indicates a slower charging or discharging process.

## 5. What are some practical applications of first order circuits with DC sources?

First order circuits with DC sources have many practical applications, such as in filters, oscillators, and amplifiers. They are also commonly used in electronic devices such as radios, televisions, and computers. In addition, they are used in power supplies to convert AC power into DC power for electronic devices.

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